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A274550
The curvature of smallest circle among 4 mutually tangent(externally) circles with integer curvature and primitive (share no common factor).
0
12, 15, 23, 24, 28, 33, 34, 35, 38, 39, 40, 42, 45, 47, 50, 52, 53, 56, 57, 58, 59, 60, 61, 62, 63, 63, 64, 66, 69, 71, 72, 72, 73, 76, 77, 77, 79, 80, 81, 82, 82, 83, 84, 84, 85, 86, 87, 87, 88, 90, 91, 91, 94, 94, 95, 95, 96, 96, 97, 98, 98, 99, 99
OFFSET
1,1
COMMENTS
4 mutually tangent circles satisfy 2 (a^2 + b^2 + c^2 + d^2) = (a + b + c + d)^2 where a,b,c,d are the curvatures.
EXAMPLE
a, b, c, d
12, 4, 1, 1
15, 3, 2, 2
23, 6, 3, 2
24, 12, 1, 1
28, 9, 4, 1
MATHEMATICA
aMax = 100;
Do[
If[GCD[a, b, c] > 1, Continue[]];
d = a + b + c - 2 Sqrt[a b + a c + b c];
If[d // IntegerQ // Not, Continue[]];
(*{a, b, c, d}*)a // Sow;
, {a, aMax}
, {b, (2 a)/Sqrt[3] - a // Ceiling, (Sqrt[a] - 1)^2}
, {c, (a-b)^2/(4(a+b))//Ceiling, Min[b, (Sqrt[a]-Sqrt[b])^2-1//Ceiling]}
] // Reap // Last // Last(*//TableForm*)
d =.;
CROSSREFS
Sequence in context: A158190 A122040 A342758 * A253235 A050480 A290508
KEYWORD
nonn
AUTHOR
Albert Lau, Jul 03 2016
STATUS
approved